It's just like in real life when two or more people meet - they talk to each other. Usually one is talking while others are listening. Then they switch places.
Below you will find some pros and cons of this compositional technique.
1. Makes improvisations more interesting because the listener can pay attention to two different melodic lines at once.
2. Creates musical conversations - ideal in storytelling.
3. Practicing dialogues between the parts when one voice is moving and another is stationary will prove a perfect exercise to develop advanced hand and feet coordination.
1. Takes time to learn. It might sound and look easy, but don't be fooled - especially challenging might be imitations and dialogues between the left hand and the pedals (practice before attempting to play like this in public).
2. Might be too difficult for beginners to attempt because of hand and feet coordination issues.
3. Doesn't work in every case, for example, in episodes of fast toccatas when the theme is placed in the pedals and both hands play on the same manual.
In my opinion, although sometimes not easily achievable (especially in the middle parts), dialogues and imitations are well worth the effort. They will make your playing more vivid, natural, and colorful.
By the way, on January 1st I was invited to play for Mass at my church where I chose to improvise a Prelude and a Postlude. Today I took the time to transcribe this soft and gentle piece for you which is full of dialogues between the right hand and pedal parts, in case you want to play it. Watch the video and download the score here: Meditation in D, Op. 36.